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Out-of-equilibrium nanophotonics

Periodic Reporting for period 1 - OUTNANO (Out-of-equilibrium nanophotonics)

Reporting period: 2017-10-01 to 2019-09-30

OUTNANO constitutes a bridge between out-of-equilibrium statistical mechanics and nanophotonics, aiming at the investigation of novel ultrafast effects in silver- and graphene-based plasmonic waveguides (PWs) and epsilon-near-zero metamaterials (ENZ MMs). The ultimate goal is to develop a new generation of low-loss photonic materials with improved efficiencies and enhanced nonlinear functionalities, including frequency conversion and lasing mechanisms, which can open new groundbreaking applications in optoelectronics, spectroscopy,
biology, and medicine. This endeavour is approached by using out-of-equilibrium statistical theories for modelling the dynamics of ultrashort pulses with time duration of few femtoseconds in silver/graphene-based devices. In particular, the project focuses on PWs and ENZ MMs, which offer the best possibilities in terms of nonlinear applications owing to their extraordinary field enhancement.

The main research hypothesis is that optical absorption in silver/graphene can be highly reduced by using ultrashort pulses with time duration smaller than the electron collision time. Indeed, for such short pulse durations, the probability that an electron undergoes a collision is much smaller and the transfer of optical energy to silver/graphene heating is highly reduced. Gaining access to the collisionless regime opens unprecedented possibilities for highly efficient nonlinear applications in silver/graphene-based PWs and ENZ MMs, whose main disadvantage is represented by ohmic loss.

The research objectives (ROs) are:

RO1. Suppression of ohmic loss in silver and graphene with ultrashort pulses in the collisionless regime;

RO2. Exploitation of temporal/spatiotemporal solitons in silver/graphene-based PWs and ENZ MMs for counterbalancing chromatic-dispersion/spatial diffraction through nonlinearity:
- Low-loss temporal solitons in PWs propagating for millimetres,
- Low-loss spatiotemporal solitons in ENZ MMs propagating for millimetres,

RO3. Enhancement of frequency conversion mechanisms in silver/graphene-based PWs and ENZ MMs:
- Enhancement of harmonic generation efficiency,
- Engineering of dispersive waves in the UV with high conversion efficiency,
- Development of SCG at the micrometre-scale through the enhancement of self-phase modulation, self-steepening, and non-local metal nonlinearities.
The work performed over the first two months of the project has focused on work package 1 (WP1):

WP1: Suppression of ohmic loss in silver/graphene (months M01 – M06)

Overall Aim: The overall aim of WP1 is demonstrating suppression of ohmic losses in silver/graphene structures by using ultrashort pulses in the collisionless regime (RO1). In order to develop this theory, the training objective TO1 will be of primary importance.


1. Training of the applicant researcher on out-of-equilibrium statistical mechanics (TO1);
2. Development of Boltzmann theory of collisions in the ultrafast regime;
3. Development of Fokker-Planck theory of collisions in the ultrafast regime.

T1.1: Attendance of advanced courses and seminars at ISC-CNR;
T1.2: Calculation of the collision-integral and derivation of novel linear response beyond the relaxation approximation;
T1.3: Evaluation of Fokker-Planck parameters and calculation of Fokker-Planck response.

The training of the researcher in out-of-equilibrium statistical mechanics (TO1) has constituted a substantial part of WP1. Such a training has been developed mainly through the direct interaction of the researcher with the host supervisor, an expert in the field, and through the attendance of the 2017 workshop of the Institute for Complex Systems at the National Research Council in Rome on October 16-17. This workshop has focused on several aspects and methods of modern statistical mechanics and its application to several research fields including economy, biology and photonics.

Thanks to such a training the researcher has developed the Boltzmann theory of electron-ion collisions in the ultrafast regime and the Fokker-Planck-Landau theory in the limit of weak coupling for a generic plasma. Such theories will be applied to describe the nonlinear and ultrafast local responses of both silver and graphene at infrared frequencies.
The analytical model developed by the researcher constitutes a substantial extension of the well-known and widely used Drude model in the context of nanophotonics. In particular, the researcher has calculated the light intensity and electron temperature dependence of damping in metals and semi-metals, a substantial progress in the understanding and theoretical modelling of absorption in nanophotonic materials. Indeed, the novel hydrodynamical equations derived by the researcher indicate that the standard damping term in the Drude model is heavily nonlinear. The results achieved by the researcher in turn demonstrate that infrared absorption in silver and graphene is heavily nonlinear and predict that absoprtion saturates when the intensity of the impinging pulse becomes of the order of TW/cm^2, which can be achieved at femtosecond time scales of the impinging pulse. The results also illustrate that the main loss mechanism in silver and graphene is electron-phonon collision, while electron-electron collisions do not contribute to heating but only relax the out-of-equilibrium distribution in a thermal one while conserving the total energy and momentum.

These initial results demonstrate the possibility to quench absorption in plasmonic materials by using ultrashort pulses with femtosecond time duration and peak intensity of the order of TW/cm^2. The potential impacts of these predictions are numerous since an experimental verification of such findings may lead to the development of novel game-changing plasmonic devices with increased efficiency and nonlinear functionality for all-optical signal processing and computing. The following wider socio-economic potential impact involves the development of a new generation of all-optical computers operating at a petaHertz frequencies, about one million times faster than current devices.
Boltzmann equation governing the out-of-equilibrium dynamics of electrons in plasmonic materials